Ratio and Proportion

Concept:When mixing mixtures from different containers, calculate total milk and total water separately using the given volumes and ratios.Explanation:Let the volumes be $3x$, $4x$, $5x$ (ratio $3:4:5$).Container 1 (milk:water $=4:1$): milk $= \frac{4}{5} \times 3x = \frac{12x}{5}$, water $= \frac{1}{5} \times 3x = \frac{3x}{5}$.Container 2 ($3:1$): milk $= \frac{3}{4} \times 4x = 3x$, water $= \frac{1}{4} \times 4x = x$.Container 3 ($5:2$): milk $= \frac{5}{7} \times 5x = \frac{25x}{7}$, water $= \frac{2}{7} \times 5x = \frac{10x}{7}$.Total milk $= \frac{12x}{5} + 3x + \frac{25x}{7} = \frac{84x}{35} + \frac{105x}{35} + \frac{125x}{35} = \frac{314x}{35}$.Total water $= \frac{3x}{5} + x + \frac{10x}{7} = \frac{21x}{35} + \frac{35x}{35} + \frac{50x}{35} = \frac{106x}{35}$.Ratio milk:water $= \frac{314x}{35} : \frac{106x}{35} = 314:106 = 157:53$.Answer:$157 : 53$, which corresponds to option C.